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For high-altitude cruising unmanned aerial vehicles (UAVs), the aero-engine components operate at low Reynolds number condition, which has a significant impact on the running of the engines and the biggest negative effects are on low pressure turbines (LPTs). An in-depth understanding of blade boundary layer spatio-temporal evolution is crucial for the effective management and control of boundary layer transiton or separation, especially the open separation, which is a key technology for the design of low Reynolds number LPT. Focusing on the blade boundary layer spatio-temporal evolution of LPT under unsteady environments, a series of research works were conducted through large-eddy simulation (LES), during my Ph.D. study.Under low Reynolds number conditions, the complex flow phenomena on LPT blade surface make conventional Reynolds-averaged Navier-Stokes (RANS) method is difficult to meet the requirements of mechanism study. As a compromise between RANS and direct numerical simulation (DNS), LES is thought suitable for dealing with this problem. Then a multi-block parallel LES code was developed, which possesses the following features: the governing equations are compressible Navier-Stokes equations and the subgrid-scale (SGS) model is dynamic Smagorinsky model. The finite volume method was used to discretize the equations, the convective terms are fourth order skew-symmetric-like centered schemes, to remove the spurious odd-even oscillations, artifical viscosity terms were added to the equations or explicit filtering operations were used, viscous terms are second order centered scheme and time integration is third-order three-stage compact Runge-Kutta method. The code can deal with arbitrary multi-block grid with matching interfaces, which has also the ability of high-performance parallel computing through domain decomposition and message processing interface (MPI). Inflow boundary conditions for free-stream turbulence, periodic wakes are provided in the code. Numerical tests indicate that the new code is of high order accuracy and able to deal flow problems with complex geometry or physical boundary conditions, so it is suitable for the applications of complex flow phenomena in turbomachinery.Fully developed turbulent channel flow and sub-critical flow around circular cylinder were used to validate the new code. Through changing calculation parameters, a wide range of tests were conducted. Test results indicate that, to ensure the stability of the calculation, the isotropic parts of SGS stress tensor should be set to zero, and values of artificial viscosity would influence the numerical results obviously, which should be adjusted according to the flow conditions of certain problems.A LPT cascade flow was simulated under conditions of Reynolds number 60154 and Mach number 0.402. Referring the experiment data available, computations for four cases with different inflow boundary conditions were carried out, they are C1 – steady inflow, C2 – steady inflow with background turbulence, C3 – periodic wakes inflow and C4 – periodic wakes inflow with background turbulence. For steady inflow cases C1 and C2, numerical results indicated that, large separation regions all appeared in the suction side rear part of the blade, the scale of separation region of C1 was bigger than C2. The transition in laminar separated shear flows of C1 and C2 were all dominated by Kelvin-Helmholtz (K-H) instability, for case C2, the background turbulence promoted the destabilization and transition process of separated shear layer, so a smaller separation region appeared. For periodic wake inflow cases C3 and C4, numerical results indicated that, because of the high passing frequency and high intensity of the wakes, flow phenomena in cascade were dominated by the effects of periodically sweeping wakes and, in contrast with case C2, the effects of background turbulence were small, so the results of C3 and C4 are similar. Under the sweeping of periodic wakes, large separation regions were replaced by small scale separation bubbles, and the total pressure loss of the cascade significantly decreased. K-H instability and turbulent spots are all effective factors in the transition process, the turbulent spots may appear before the separation point, or appear in the separated free shear layer, and the structure of the spots looks like a series of vortex loops.